{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ungraded Lab:  Overfitting in Logistic Regression.\n",
    "\n",
    "The lectures describe **Overfitting**. This is when the model follows the data too closely and does not generalize well. In this lab we will explore overfitting in logistic regression and how regularization can improve situation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Outline\n",
    "- [Tools](#tools)\n",
    "- [Dataset](#dataset)\n",
    "- [Polynomial Feature Map](#FeatureMap)\n",
    "- [Fit the Model](#FitModel)\n",
    "- [Reducing Overfitting](#ReduceOverfitting)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overfitting\n",
    "In this lab, we will explore how overfitting happens and what can be done about it.\n",
    "- Create a logistic dataset with an irregular boundary\n",
    "- Create an overfitting problem\n",
    "    - polynomial Regression and Feature mapping\n",
    "- Regularization to reduce overfitting\n",
    "<a name='tools'></a>\n",
    "## Tools \n",
    "- We have not yet developed all the capabilities to do gradient decent with regularization so we will utilized sklearn's LogisticRegression capabilities explored briefly in a previous lab. \n",
    "- Plotting is very useful when exploring decision boundaries. We will utilize matplotlib. Producing these plots is quite involved so helper routines are provided below.\n",
    "- We will create a polynomial feature set. `map_features` is provided to simplify that process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(X, y, pos_label=\"y=1\", neg_label=\"y=0\"):\n",
    "    positive = y == 1\n",
    "    negative = y == 0\n",
    "    \n",
    "    # Plot examples\n",
    "    plt.plot(X[positive, 0], X[positive, 1], 'k+', label=pos_label)\n",
    "    plt.plot(X[negative, 0], X[negative, 1], 'yo', label=neg_label)\n",
    "    plt.legend()\n",
    "    plt.xlabel(\"X[:,0]\")\n",
    "    plt.ylabel(\"X[:,1]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_decision_boundary(x0r,x1r, y,predict):\n",
    "    \"\"\"\n",
    "    Plots a decision boundary \n",
    "     Args:\n",
    "      x0r : (array_like Shape (1,1)) range (min, max) of x0\n",
    "      x1r : (array_like Shape (1,1)) range (min, max) of x1\n",
    "      y   : (array_like Shape (m, )) target values of y\n",
    "      predict : function to predict z values    \n",
    "    \"\"\"\n",
    "\n",
    "    h = .01  # step size in the mesh\n",
    "    # create a mesh to plot in\n",
    "    xx, yy = np.meshgrid(np.arange(x0r[0], x0r[1], h),\n",
    "                         np.arange(x0r[0], x0r[1], h))\n",
    "\n",
    "    # Plot the decision boundary. For that, we will assign a color to each\n",
    "    # point in the mesh [x_min, m_max]x[y_min, y_max].\n",
    "    points = np.c_[xx.ravel(), yy.ravel()]\n",
    "    Xm = map_feature(points[:, 0], points[:, 1],degree)\n",
    "    Z = predict(Xm)\n",
    "\n",
    "    # Put the result into a color plot\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    plt.contour(xx, yy, Z, colors='g') \n",
    "    #plot_data(X_orig,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def map_feature(X1, X2, degree):\n",
    "    \"\"\"\n",
    "    Feature mapping function to polynomial features    \n",
    "    \"\"\"\n",
    "    X1 = np.atleast_1d(X1)\n",
    "    X2 = np.atleast_1d(X2)\n",
    "\n",
    "    out = [np.ones(X1.shape[0])]\n",
    "    for i in range(1, degree+1):\n",
    "        for j in range(i + 1):\n",
    "            out.append((X1**(i-j) * (X2**j)))\n",
    "           \n",
    "    return np.stack(out, axis=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='dataset'></a>\n",
    "##  Dataset\n",
    "Below we create a logistic dataset with two features based on a quadratic. Random noise is added to create a scenario where the model can overfit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 500\n",
    "n = 2\n",
    "np.random.seed(1)\n",
    "X_orig = 2*(np.random.rand(m,n)-[0.5,0.5])\n",
    "y_train =  X_orig[:,1]  > X_orig[:,0]**2 + 0.2*np.random.rand(m)   #quadratic + random\n",
    "plot_data(X_orig,y_train)\n",
    "plt.title(\"Logistic data set with quadratic boundary with noise\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='FeatureMap'></a>\n",
    "##  Create Overfitting...Polynomial Feature Mapping\n",
    "In real data sets, the boundary between \"True\" and \"False\" features is rarely a straight line. To create a non-linear decision boundary, our model will need to support non-linear features. Concretely, if we have two features in our feature set $x_1$ and $x_2$ we can build a model of degree 2:\n",
    "$$f_\\mathbf{w} = w_0 + w_1x_1 + w_2x_2 + w_3x_1^2 + w_4x_1x_2 + w_5x_2^2 \\tag{1} $$\n",
    "To do this, we must convert our two feature data set into a 6 feature data set, noting that,as usual, $x_0$ will be set to 1. The routine `map_feature` was provided above to do exactly this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape before feature mapping: (3, 2)\n",
      "[[2 0]\n",
      " [0 3]\n",
      " [2 3]] \n",
      "\n",
      "Shape after feature mapping: (3, 6)\n",
      "[[1. 2. 0. 4. 0. 0.]\n",
      " [1. 0. 3. 0. 0. 9.]\n",
      " [1. 2. 3. 4. 6. 9.]]\n"
     ]
    }
   ],
   "source": [
    "X_tmp = np.array([[2,0],[0,3],[2,3]] )  # values selected to illustrated equation\n",
    "print(\"Shape before feature mapping:\", X_tmp.shape)\n",
    "print(X_tmp, \"\\n\")\n",
    "\n",
    "mapped_X =  map_feature(X_tmp[:, 0], X_tmp[:, 1],degree = 2)\n",
    "\n",
    "print(\"Shape after feature mapping:\", mapped_X.shape)\n",
    "print(mapped_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the results with equation (1) above.\n",
    "\n",
    "Of course, we don't have to stop at two. The `degree` argument to map_features will determine the degree of the polynomial that is created. The degree will be determined by the complexity of the curve you are trying to follow. Increasing the degree will allow the model to follow more irregular boundaries, but can also allow for overfitting. The number of features/parameters grows exponentially as all of the cross terms are included. Sklearn [`PolynomialFeatures`](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html) can also be used to create feature maps.\n",
    "\n",
    "Lets convert our dataset above to support degree 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original shape of data: (500, 2)\n",
      "Shape after feature mapping: (500, 28)\n"
     ]
    }
   ],
   "source": [
    "print(\"Original shape of data:\", X_orig.shape)\n",
    "degree = 6\n",
    "mapped_X =  map_feature(X_orig[:, 0], X_orig[:, 1],degree)\n",
    "\n",
    "print(\"Shape after feature mapping:\", mapped_X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note, with a degree 6 polynomial, we now have 28 features!\n",
    "<a name='FitModel'></a>\n",
    "## Fit the model\n",
    "\n",
    "We are going to use the `LogisticRegression` feature of SkLearn that was introduced in a previous lab. One thing to note, this routine has regularization built in. We will enable and disable that capability to highlight aspects of over fitting. To disable it, the command line argument `penalty` is set to `none`. When enabled, the `C` command line argument controls how much regularization is used. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "# create and fit the model using our mapped_X feature set.\n",
    "lr = LogisticRegression(penalty='none', max_iter=10000)\n",
    "lr.fit(mapped_X,y_train)\n",
    "\n",
    "# print an evaluation of the fit, 1 is best.\n",
    "print(lr.score(mapped_X, y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a trained model, lets map the Original Data (not predicted) along with the decision boundary we derive from the model. Examine `plot_decision_boundary` above to see the details of how this is accomplished."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary([-1,1],[-1,1], y_train,lr.predict)\n",
    "plot_data(X_orig,y_train)\n",
    "plt.title(\"Example of overfitting, degree 6, no regularization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, the model has done an amazing job of separating the data! However, that is probably not what is desired. \n",
    "We can take two approaches to reducing overfitting:\n",
    "- regularization \n",
    "- reduce the degree of the polynomial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='ReduceOverfitting'></a>\n",
    "## Reducing Overfitting using regularization\n",
    "The next labs will cover regularization in more detail, so we will just explore this briefly.\n",
    "Lets fit the model again, but this time include regularization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fitting score: 0.966\n"
     ]
    }
   ],
   "source": [
    "# create and fit the model using our mapped_X feature set.\n",
    "lr = LogisticRegression(max_iter=1000, C=1)\n",
    "lr.fit(mapped_X,y_train)\n",
    "\n",
    "# print an evaluation of the fit, 1 is best.\n",
    "print(\"fitting score:\",lr.score(mapped_X, y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pGEIXxmnA765/l6Ezh7LqfS9t3WbkdWAXCIZar2eL/ubmZlS1e3Fk/a72/aqd8JOiK0i5SYzLOJA0bR9s+oDRvxzNm2ve7L42clDo0GHxw2r8rD4YR3m+6HLv88DdGOdBfAJ4wrw+HOOo2WHm5zVguF9ZEyeic+agDz44SFtbb9IFKxdov+Z+SjNKM/rNu76pYWFUYTyIM6+8Y/r06Qr0+EyfPr2qPIMgrnpO4h2CwIl+p2tR6UijTyddd3keS0nQdsm8S7rnMZrRJ5c8GWv+wHyNMr9HeSiuD8b568uBTRh2lFOBM4AzzPsC/A7jEKcXgMm2Z6dhnH++CDglSHkWg5kzB3300bGqqjr9gellDXPW3WeFrXgjnxgGRhIdL+nJLiqSmGCC1p9XuqQn5aT6iVO+YfpTUhN+kOeT6PdxMty4Eff7/vyRn5fNYSf97aRY81etUQaT9sfOYObMEVVV7erq0tP+cVpZA23o2BC44q1OG7XT9OWVnIW4aPRaLQet56i0xMHcvBClnyT9LnEhrYVVXsZC3IyubkZd99z1X3/8L+3o7Ig1f9WCwYRmMJYEY2HQhYO6G+lDF35IX3/n9bANECp9UnmkkWfcqIbGIBNvZf5e5VXDAIIg6X4Sx4Il7T6TlmRRC2MhDFa+t1JH/nxk97xV11ynXV1diZRVMJgQDMaywdjx0oqXtOH8hu7G2u/a/brvuQ2AuKWPWrcNREXS0pofg0m6vrLqJ0kzy1pAmmMh7Xo7/rbjy5jLI288klhZBYMJyGAefXRsGXNpbb1JH310rM6ZI/rAQ1vpwb/brCo74/YzrMoN0gC+aZxg75RJdNBaWbXFbZvwmljiVCuFpTuO9ohTWupNzMQPSY2FatXkUdA8p7lMrX/V/KsSLS8qgxHj2b6ByZMnq/1Ey7a2m3nlldPp6nq/+1qHlpjZ0sn95p7MF7/2IruO2hW/ehIR3zRxPpeX/ONCHHQ2Nzc7un2GyTssHUmnD4PK93erj7ToyRuSelcr37Tqsm1dG6N/Nbr7/2c//Fnu/O87KdWVEitTRJ5S1clhn8v7PphEsXjxuWXMBaBeOvnajvUwB2iGXUftCvj7rU+fPj1ZYiMir3SFQdC9AnHsKUi6vpLMv3L/Sh72f+QJSdS9Vcdp7b1pXdvKRy7/SPf/xoGN/N+J/5coc6kKUcSeWv3sueeeZWLfnDli8yor9zCz22OIWfStNRtJUojTs8ur7uKu17y2X9B+mlf6awnV1mHYuu7q6tLv3vPdMrVYXXOdzntrXnjiI4BCReYPu4qsre1mWlqmAp090jU0jGXCx+Yz8hfmTthm+PodX+fSwy7tXqnEhb6kovCCVz0EqaOs6jHr9mtubnbceT99+vRAq+is6e8NiKIiC1vv/7fw//jcHz/X/f/zEz7PP4/7Z2qSS6EiCwHL9uLEXOrqBjF+/IWMGDSCaZOmGRcPhN/N/x2DLxrMyyteTpfYPoqsw35UlpNGuVHKqAzLMn36dFSTD8uSFfL8XkmpP998902O/svR3f8P3P5A7vjvO/KrFrMjithTqx9LRWZ4jTmpxko93JdfbHtRB54/sFssLc0o6abOTd7yZAhkoZbIoyokimdXkqqeyjK9aIgLbmWEeT5sHkmoD5Msq9o6SgJh1GJu/dXuzVrp6fqhCz/UPf/0O7+fLli5IKE3cQeFiswflops7tw6jLathDBlSlePq6pK/fn13cExT/7YyVx3xHWxq8vSQq2pRbJQkVXmJyKB1U5hYXl7VfsOlrosy7atVtVZTf5eCOJRlybs7+HkzVpXN4iddrqaS19s4cJHLuy+3nleJ3WSvuKpUJGFQEPD9qGuiwjnHnBu9//rn7uek/95chKk5RJZD8y0POHc1HLW/xkzZsSuprOYQjWqQItuyxaTpyjCcSAOdWlejwRobm529Gbt6nqfZ1q+XsZcTp10aibMpSpEEXtq9WOpyFpbb9IHHxxUph5z2t1fiWufunazB8eMujJR1UvEzQOqUSeRQ7VEJeJW9VS+MxHUT2HLiiP/LNrKb1Nr1H7nhKjvV229hKE3SFr75kw3b9b7H9jsMfbrez+f6fxCsZM/OINRjcYQ3tv4ng796dAyV8Fla5ZFZlhZIexgqwUGEzesd07KzpNUvna6s4BXX0mbgcZZx2HKDZvWzSb8p7uNOeazl5d07oMDPeeXpBe4URlMjclb8WHUqBPYZ5/XmTKli332eZ1Ro07wfWZQv0G8c847bNl/y+5rX7/r6yxe/ENHEXfx4nOpVYRRS1SjismTGsfpnWfMmMH06dO71XTWwInjcDkrLytfJxtP2HIsOvOqEqoWYdSlWRx8FiTvyn724x+/wfr15WnWd8I1iw135OmTtkW7Pii7b59fLBvOhg1vAMqGDW/wyiun09Z2cxyvVB2icKVa/VRutIyKy5+4vEyKuf8BJ4+0zUcC5A1xx8/yu5/Us0nCia6kaPXKN2qZWdVrFC+yNKStKPURRgKKKi1ZdLW23qQPP7Kt3n+/Ibkc/Dv0ny3/VFXvDeGq7l6xlRHjqwGFBJMevrbX13jhjBcYUDcAgBUbnNO5OQ1kjSylhjxJLGGRlLNBXPlmvXfIoiHsvTSkrSh1HEYCstJa8ErrhHdLkzngvqUcfDAc/zg8uXoIn5tgbKz0c0rasOFNx/tu19NEwWAiYtdRu/L+j97nY1t9jGsWGyKtHdaGzTQQ1uMoLJwGZ9TJbMaMGbmYCP3g9s5JwEktFqV+rEkubnVeb0DSajF7ewGB+7OlFt155M5gJW+GNT9cw4U/MeaP8eMvpK5uUNlz9vklrFdsqogi9sT1AQ4FXsE49vgch/sXA8+anwXAu7Z7nbZ7s4OUF5eKzI77Xr1PaTZE2j/djT7wAProo9unauAnIQNkGuUnQU8SSEqNE1SFEgYk6PEWF/IQDy1uzzBVjfQOe161Z1ncw+ufub5HGi8jfhpORtSaFxlQAl4FxgP9geeAXTzSfxO4zvZ/Xdgyk2AwqqqvvP1KmU3m6WVPJ1KOG/LOYLwmE/uzeYwwYCGpCdsv36gMJs91WYmsmGHWiy1V1eVrlpfNHVFpyqsXWZYMZh/gX7b/PwB+4JH+UeDTtv+5YTCqqh+9/KNlHeXLf/tyYseXqqZjgAxDS1BUDiD7s3ledWfFYOIIQ5J39CYGE7S+u7q69Hv3fK9szhj9i9G5ba9aZDBHA9fY/p8EXOaSdiywHCjZrnUA84HHgCM9yjndTDd/++23j6u+e6Crq0un/X1aWYfZcuaWun7T+sTKtJC1BBMGXuVnTVslqpm0/bypkmQGeatHP6StFsuaEXd2dep2v96ubK74/M2f147OjtRoCIvezmDOBi6tuLat+T0eeB34sF+ZSUowFha1LyrrONc+fW3iZabJYOLYYFj5P+sBHwRh6816hyRsLEHK7o2Iu0841VMa/e7+xfeXzRFPLX2q+15eI4LUIoMJrCIDngH29cjreuBovzLTYDCqqsfcekxZB2qe05xoeUkYK92eS3LyyvPEGIXBWJ848w2CvDHnuBB3XTnll2Qf7Orq0rPuOqtsbvjE7z/RfT/PEUGiMpgs3ZSfBCaIyA4i0h84DphdmUhEdgaGAfNs14aJSIP5ewSwH5Cbg1r+fPSfN58lA/zkoZ9YjDARJO2mDM57FeJw/awFl2UIto/CyV3Vul5NvmGRt7rLK5La1+SEdRvXMeLnI7jkiUu6rx2181H8+9R/d/93C3q5cOFZrvm2td3MvHnjmDu3jnnzxuVj974dUbhSXB/gMAz341eBc81r5wOH29I0AzMrntsXeAHD8+wF4NQg5aUlwaiqfrDpA5Vm6V6pDLpgkD7f+nxq5ccJNzUWKawoaw1edRWHZBElj1qWaNJQoaZRxvlzzy876viF1hd6pHHfsY+jFJOmxENxHow/7Ecmp4EFKxewx5V78F7ne93XTt/jdK76r6tSo6EaWKHkK2FtDotyNofXuRy1dk6NF+xSTJzvFKWOsqrXuM9gSeM94i5DVfnaHV/jqqc3j/mvT/46l33+sh5p580bZ8YT64mGhrHss8/rgdI7pa0WxXkwOcTEERNZe+5aztprs4h79dNXs3bD2gypCg6nUBlAVeeXeIUFSVNlkTR607tERW8NuBkUS9YsYchFQ8qYy5c+8iV+e9hvHdN7Rf5wCvviFyImD+qzgsEkDBHhN4f9hqENQ7uvjfzFSJ5e9nSGVEXHdPPMdzvTUY0nHElvsh00NzeXRWGuNq+wdiqvZ6qN2JwV0mDacZZx2uzTWLdpHQD96/rTcmYLtxx9i+uhYaNGnUCp1Oh4zynsi1eImLxEWO5zKrI77/wOixefy4YNb9LQsD3jx18YKFR/tVjUvog9rtqDtZs2Sy9H7nQkf/vS32ri6GWniSmoOsFP1VYgOOJQkfn9rwZFWxuLrmmzp3H9s9d3X7v16Fs55iPH+D7rdXxy5TzlldaY4+JTn0VVkfUpBvOxj43XSy9tC9R4SUBVOefec/j5vJ93X3tk2iPst91+iZedBKLo2HuTnSUL5J3BeJXbF/BS20tMvmYy6zs2H/Byym6ncO2R1wZeSLa13Rx4EeyWdu7cOgxfhUoIU6Z0hX6vgsEEQFNTg15xxcYe15Mwinlhr9/vxfxlhrNBfV09U9+ZyjW/via18rNEX5x04kQUpm6lD2ITiVPS6IttPebXY1i6dikAW9RvwTNnPMOOjTumTkfcDgCFkT8Aurp6MhdI/9yEf3zpHwwbMAyAjq4Orr34Wg6ZdQgdXR0AXH75FzM3zoVBmAmpVozfeVXnRKHLYkpOtrMkbGkWaqWt40CXdnHCX0/oZi4AL33jpUyYC/iH+E8LhQRD+hKMhR8/8GMuePgCY6dPM5SkxB3/9W1o+xUDBmxOl6YaLwisScj67o0r1d7i2uuEtFRkfQVPLH2CT/7hk2zo3Hzy4Df3+qart1g1iEN9FgWFBBMA/ftvmwuuDsZEcsHBF5QdMtQ5vZN33yhnLlB+/nbcNETBjBkzUnVBjWvCzatUYkcWpzvGeaJmX8T+1+3fzVyG9B/C4m8tToy5hPEMGzXqBPbZ53WmTOlin31ez2SB2qckmCy9yLwgIpQOKtE5p5P774c6R7YfzTjnV26UjZJ+e1ninmjiWmH75ZMHD6haliZqmfYo6NIujr31WP76n792X9Ppyb1/mhsrK1FIMAGRB67uhN//6vfQDCuczUSZH39q7atwYy52HX6trmTd7BRJv0+txGMrsBmPvPkIAy4YUMZcLjjogkTL9NtYmUf0OQaTR0yfPp1Tdj+F9u+18/flw1m/vvx+Xd3A2NR4UScza/K1wz4Z2xGHmieuSbcWJu+sGFscqIX6jRObOjcx5fopHPCHA9jUtQmAYQ3DePPbb3LuJ+NXY9vhtbEyt4gSwKxWP2kGu6wG371gd/3T3ej9D6B/uhs9+rotEymHgMEl/YIBVgYFDJpv3HTGmU8SASKD5Bl33aWJMP2pVgNwTrpyUlm4/QvnXpha2VmG86fWzoPJ4rPzzv1zd5CPG1asW1HWkf/8wp9jLyPKZGYxliQODnNLmwWDSQJByq/ViVc1eP1afcMLeayH+18tPyjsueXPpU5DVgeSFQwmwGfixPwd5OOF/a/bv6xD73zpzrpm/ZpQeXgN1AMPPDA0TUEmkagTudtzYc6lr+Z+0qj2/fKOoO8RhMFkvRiwY/2m9brPNfuUjcWJv52oXV1dWZOmqukwnYLBhGQwc+agjz46NnKFp4Ubnr2hrGPTjF72+GWBn/caqFEGcZJqnmonlTxNShaCSHZp050FQwt7Tk5e2vLWF27Vuhl1ZePvl4/8MmuyupGW2qxgMBEYzJw5Er3GU8T7G9/X3a/YvayTb/urbXXFuhW+z/oxmKxsDfa01arWLORdBeVGX9qTadaTt5sEk8bBX0GxZv0abbqsqWzM7fDrHfTdD95NnRYvGJJLzwPK4l48R2UwfdqLzO59EfbshDTPWhjYbyBPn/E0dx5/J4LhrbN07VK2+uVWnDfnvB7p/UK12+9ZZ7vE6fUTJq9qPajCejHl5YySvuZ9FQR58aa7/InLGTJzCC0rW7qvXX/k9Sz+zmKGDhjq8WT6yLvrcqYbLUXkUOASoARco6ozK+6fDPwCsAL8XKaq15j3pgI/Mq9foKqz/MrbaSfRq8yzf+rqBjF69FTa2+8yNy8J9uijXuFZwoTUrgZOoR4aR36JQ284lPvfuL873f7b7c/D0x52zMNr85s1uWXZB+yodqOe9bzXXpwsNwO60ZUGTXnYRGqnxf7thCzaaeX7K5l05aSyeGKTtprE7MO/xZI3Z+Rqc7YFt82X9fWNlEpbxEZzzUVTFpESsAD4NLAEeBI4XlVftqU5GZisqt+oeHY4MB+YjMEVngL2VNV3vMo0YpFtoqFhexobD6O1dVYZk6iE2w7ZNHbUujGxzUzxTVrXK9cshvvfhuX/s5zRg0f3yMdpoFYz2SS5kbLavK13rXznKVOm8OCDD/ZIn5czSsKcq5NE/eQRaW/Y/c/b/2GXy3dBzUWmINxx/B3sOfQd33GYJdNxmidE+pvtu6mM5moWwLXIYPYBmlX1s+b/HwCo6kW2NCfjzGCOB6ao6lfN/1cBc1X1T15lTp48WefPN8Lke51/bSvJMTxL3GctOMGdvnJJa30n/PIVg8l8f9/vM/OQmWXnTngNVIvRhOkDeZ6c7CpAO432/3mk395GSUpftcRg0sahNx3Kv179FwCjB43mrf99i/q6+sDjMMuAtJWajo6OdXR2tvdIV80CuBZDxWwLvGX7v8S8VokvisjzInKbiGwX8llE5HQRmS8i899+++3u60F0lGF3zsa5o9advvKJYUAJThtv/P75oz9ny5lb8mr7q933vVaBeVi9xwWLWdaiTcNOY9w2IidbT2WZfRmta1vZ+pdbdzMXgJmfnkl9XT0QfBwmFZA2CCrDX3V2rnJMl4VdJu9G/tuBcaq6G3Av4GtnqYSqXq2qk1V18siRI7uv+zEDryjLaZy1EIZZjR4g9K/rD8CajWvY8bIdmfr3qYFWqUEi6cZhkK5MG/cEV2kgtt7LmrAtmg888MBYyw1KWzXPBql7Lyk1D4ZzJ2TlWAJGPZxz7zls/eutaX2vFYA66rjnhHuYOmlqd7ow4zAvhvU8hZTJtYqsIn0JWKWqQ+NQkTnpLi2xt6FhrK9ONc6zFpywYMGZLFt2RaC0DQ1j+cQnXmPaP6Zx/fPXd18fUBrAv6f9mz222SM2uqKqV9I8gyRv553EFcXZz2HD7x2zrodKhKUnLvXhq+2vsufv92T1htXd1z634+e4/fjbKdWVytJ6zROVyOpcqUok4YRUizaYegwj/8EYXmJPAv+tqi/Z0mytqsvN30cBZ6vqJ0wj/1OANXM+jWHkd5YNTdgZDCTPJKLCuVM7o7LjLGpfxB5X7cHaTWu70xy242HMPn52j8ETBbXAYConIq+y0jAmh3nXqEwkSBlpG879ELYPVPv+qsqps0/lD8/+ofta/7r+PHrqo+y5zZ6uz1XOE04OQnk7FDDuuS0qg8l04yNwGAaTeRU417x2PnC4+fsi4CXgOWAOsLPt2WnAIvNzSpDyaiXYpdvmqcpNom5hIbq6uvT7//p+2Sax+vPr9Suzv6I/fuDHum7Dusi0xbGJsvKT9EY6r/xJaNNh1E2DXvQkEf8tbVRDc2XdhMnr6WVP64ALBpSNial/mxo53EtWMcGyAhE3Wva5A8fsEkxe4e6lZiCoKN66tpXdrtiNtz94u+y6IFz1hav4yp5fAdKR5PKmtkqTjjBlRJUy8lKfYRBU6oqqPnz0rUe599V7uf+1+3n4zc37xLbotwVPf/VpJjROqO4F+hBqTkWWBfwYTF5UZl4u1FFE8V/9+1d8977v9ri+/ZDteeCL57L09e8kLu7nicGkvekwb0zMD2mp0pJSkb238T32uXYfXljxQo9039vne/zs0z8rc+Uv4I9adFPOFcKed50knLzUAEqlxkgT///u9790ntfJ2h+s5e/H/r073Myba97kyZe/2sPWk4TLZVLnwEdB2p5VabxrnGWkFU4nTpqtvK55+hoGXzS4B3MZOXAky/9nOT//zM8L5pIiCgZjYvHic1OZaINg1KgT2Gmnq2loGAsIDQ1jaWq6iQMOWBlZqqiTOrbovwVHNh3Jhh9t4JPbfRKArRqc08ftchnGTTnJ1XMWRu40yvRyU84r7JtLg8BiIk7pv/X9b7HDb3bgK7d/pXs3/q6Nu7LkO0s4e9PZvDD1Yl578ROpxA6sBmnGOEwDhYrMRBq78/OGR958hKUvH8CoAT3v1fcfw/77vtXzRoxwU8Wk6cKcN8+qoAhKd5gwNFnFKouqKlv5/kpeaX+FO165g5n/LgtjyD++9A+O2PkIAA45RDjvvEGxqYGTUqWnFeMwCgobTAB4MZg04ovlEctbb+LFlpPpJ53d16zwM/2Hfo7Zx8/u3tUcN9wmljQZTK0i6HtEed8oz1TDqKMwmC//7cvc8PwNPe4dMOYA7j/5fvqV+nVfu+UWYXTPMH2RxnaSTCDPc1Bhg6kSaezOzyO2Hn0iu+0yi7r6relSaF2/ObbZ3YvuZuCFA/nby3/jzdVvsqlzk3+GERFHtICoeU+ZMqXqMvKEJOvSDWHtNmFprEx/w/+7AZoxNi8AJUo8dPJDPHTqQ/Qr9StLv9VWzjREUQMnqUrPe+j9KOjTEozTBqo8REjNCqrKI28+wsr3V3LG7Wew4oMVZfcF4YrPX8FXJ381chlBVDFpSzC1ItVEUWOlJY1UU4d+z67dsJb3Nr3HtH9O4+5FdxuMpRkG9xvMNYdfw4gPjWDKuCnUifN6OU4JJklVelQJJqVtBoWKzA9+oWLS0HfmxRU6CC2/mfcbvnPPd3o8t92Q7Zh36jyGDxzOwH4DI5cfRkUWl60kawaT5HtUky4K4rLbuNH43sb3+Pg1H+elt18qv9EMZ//rbC769EWBPMLitME8/PCI2CMVW4gyJ6U1jxUqspBwE3VbWk5MzHsjT67QQWj59j7fZvU5q7nisCs475Pndbs3v7XmLcZcPIZBPx3E0IuGsmDlglhpc3Jfjct11sp7ypQpjiqapNVlaZ+omaSLdBh3by/vKDuNVh5Xzb+KwRcN7sFcRg4cyf/+4H+Z+ZmZgZgLwP77T+/hlRllAm5ru5murrUOd/rFokp38h71ozNP3q9O6LMSjN9u+SRWAXky4kWhZVPnJj4969M8+FbPw7tO/OiJzDpqlquawglxxeiqFmlKMHGVlTfvN6/3CrLKVlW+e+93+fW8X/d4fufGnTlml2OYvM1kDt/58GReIAC8To/cf/+VGVCUnvdrIcGEhF/o6iRWAXky4kWhpV+pH3OnzeXp05/mm3t/k8+M/0z3vZteuInS+SVkhrDfdfuxoWND1TRGNVbnaeKFZIzueXtHL0nJfZX9Q4685UhkhlB3fl0P5iIIs4+bTcs3Wjj/U+dnylzAfWx0dHjG2E0UeQrN74Q+K8EEi1gc7yqg1iUYJyxetZjdr9qdNRvXON7fYcsdeOr0pxg2cBgQXW+fpLQzZcoU5s6dGzh9NUjbBTgPcFtldykc/FD5tf51/Tl6l6PZfuj2nH/Q+WXuxlkjT+PXQt5tMH2WwYDdyO0c9ysuw51lSC+VhtPVtRbVjd33s9pIFXfHvPTxS7l38b3MXzqf5e8t73FfEIYPHM7jpz7Ohxs/bFxLiGnk2SssrX0pQZAW43rk0e3o2Likx/XW9XD84zCs/zD2H7c/e22zFz/65I8yC+Xi5/SS142QhRdZTuC20TKpjuMsJfWjvn4IHR2rEusMQTtcUh3zlhdu4fL5l7N09VIWr17c436d1DGwfiDvnftebFGGs9yJHgZpuwBnkS/Aiyte5JN/+CSrN6zmoBFdfHcn43hvCxs6hdntE/nIuG9x5t5nJkJDGASdA7LwAs2D52nBYALAayd/Eo0Yl0gdhjY31V+p1MjEiZek3jEfeuMhvnvPd1nzwRpeeeeV8ptzoPSpzbPO9kO35/HTHmfkh0ZSDfIswQRFGgwz7nq6e+HdHPOXY1jfsZ5O7Sy7d/BIOGPHehr7ddBVGsmuO12cqz1maau/wiwC8yA1FQwmANI+D8bbU00CMbKwHSzuUP9xYlH7Io6/7Xje3fAui95Z5Jquf6k/WzZsyZypc9hlq11Cl9MbGIwdcYfij4NxLVm9hP2u26/7PHtVZVNXz0gPOwzdgcH9B3PtkdcyeZvwByKmgba2m2lpOdHlbvyxCMOM6SCMr1CR5QRpMxivyd6C36QfdmUV12FlSWPV+6v4wp++wJI1hm5+/ab1PQ5GAxhYP7B7/81HtvoIc6bO4UP9P+SZd5K2hSwM7mECVsaxwbESGzo28IU/foFH33oUAEX5oOMD1/Rjhoxh5MCRzD5+NmOGjglMTxbwc/ZJYryEGdN+bsiFkd+rcJFDgUuAEnCNqs6suP8/wGlAB/A2ME1V3zDvdQLWoQ9vqqqvD2PaDCaYp5p3Jw7r5+7P1PIRHdpp1fXGpgkc85djeG/je7Sv77lb2sKQhiFl/wf1G8Rfj/kr+26/b9JkZyIdxR052S/9eXPO49InLqVLjX6ydsPa7hD4lRg+YHj33qcdh+/IPSfdw+CGwYFpyBpxS/xBHAXCSEt+zCgt1V5UBpNMmNwAEJES8Dvg08AS4EkRma2qL9uSPQNMVtX3ReRrwM+BL5n3PlDVSWnSHBZWx7I6nJtk4bX3pKFhe5fNXcMd048ffyH/+c+0Mk+1yvyyRiXjtaII7LTT1bzxHeNd33jnDQ6+4WBWvG/EQ+vo7OCDTmPVvGZDuUv0mg1r2O8P+7HlgC3pV1fu1nryx06u+RMMk5CY1m1Yx3aHb8dWvyiPBLlmwxo2dDrvYWooNdC/1J9PNm7k5LEdjGjooqFhcE3H7PNajDkxFy8G4tavwZgLrPtucBqbjY2HsWzZFY7XjTLys7fOCZkxGGBvYJGqLgYQkVuAI4BuBqOqc2zpHwPcWH8gvPfeC8ydW5eqJ8aoUSd0l+O+2nCf9N0YRkfHGtrabnZ8B7dVbF6iQ3uFt7DeZ+ywsSw6q9xOc/srt/Plv3+5bAJUlPUd6wF4d/27Pcr6xbxf8NsnfstWHyqfSMduOZY7jr+Di2deHGjjpt1uYTGrPHioudH2wx/9kKd3erpnHC+MOluyZgnsAXgI1wPrjThz9XX1XPyZizl1z1Ntk6jRBpWTaBJI1sZQAjodrzsxFy8G4tevne5bcBub7e13Oaa3rrstQPOwkIQMVWQicjRwqKqeZv4/Cfi4qn7DJf1lQKuqXmD+7wCexVCfzVTVf7g8dzpwOsDEiex51VXG9SwM3lH1pWEC7LmL/CWammblYhKIO7zFqvdX8YlrP8Hr775edt3J6NwDzTDx0omByjlw+wP5/RG/z8yBYMV7K/jin7/YLdVVYsE3FzDx0omoKotWLXJVa9lRTz1St1m6ExGObTqWWf/POexPtSqZsHaiqAEgg/dFd8l2ypTy+vN7d79+7WUfbWq6yZHGWrfBZCnBBIaInAhMBg60XR6rqktFZDzwgIi8oKqvVj6rqlcDVwPstJN0t1TlijkNVKrMgq7GOjudQ1E4icHuonFXoszFa2VXibhXXcMHDWfBN3sG3FRVvnr7V7numet6TLZdbGZkC9qDBeu00k26clLqKreNnRt5+e2XfdNVvkudSzSo/qX+3HbMbXx+p8+HoqNalcyMGTNCMZgg0q4d4fviWFemUQm/d/fr1+73x7qOTb88o84paSFLBrMU2M72f4x5rQwicghwLnCgqnbrRlR1qfm9WETmArsDPRiMF7LQU9pVZkERZkLOQmQOOwmMH3+h46orbvWdiHD14Vdz9eFXl13v4arbbH6byxc5qCfz6GZQB8Jzbc8FJ2IOcFDw5EFgedVVQg/U7nv1dfXcdNRNHLvrsbGWnXb/CsvQkuyLfu/ul1eUfh/kmShzSlrIMtjlk8AEEdlBRPoDxwGz7QlEZHfgKuBwVV1huz5MRBrM3yOA/bDZboIiL3pKP4Q5bTOLkznDTgJRwpLHCbcw8zpX4UHomt7V46PTlfMPPN+R+XiiZ+DpyBhUP4gnT3vSkb6u6V3oXO3+vfHHG6tmLk6SRpT+VU2wz7DBHMP0RUuVZkzeJTNf977o9+5+/TpKv896rFSLrN2UDwN+g9G616nqhSJyPjBfVWeLyH3ARwEruNWbqnq4iOyLwXi6MJjkb1T1Wr/ydtpJ1LLBpBGyJU6E3c2fpsicxyCAQVHpqhu3G3Itb/p0o72a/hW2PuLaaFzZF6PaLvIQtiUL1OQ+mLTR1NSgV1yxKVdBJ3sD8haeJgysVXScYVlqJS6aH5JgjlHyrDZUktPYrpVFUV4YWsFgAsDaaFkrnatapNk529puZuHCs+joKPd2qzXGbU2AcdVdrUkwSTPHNCIhBGm7tA7qqgZ5iUMGBYMJBIvB1ELnqhZZdM7ewLhFhNbWmxwkMgGUhoaxiaqE8oSwtNfSuTW10FfzRGNxomUI5P0UuDiQxVndedtVHGWymz59usuGOGOitdxe7WfK++XXV+Ak+eQVaTvDtLXdzLx545g7t45588YF6j95G09R0CcZTBaeVmkji86ZN8YdZcJrbm72raMwjDqPK/qgNEVljlEm07SRpneWpU0wpBENvEjJ23iKgj7JYGrd9S8I0uyc1oRiDKByN95aZNxB6qiWVpGVCMp4gzCiShfkQw4RnnnmRN/JNA9MaNSoE9hnn9eZMqWLffZ5PbHxH1Wb0BsWwp4MRkRmB/hcnxKtsSKtzpUV0uqc5aszMFRJxmQThHHHPdFE2XNRec+p7ipRS6vIJFG5p+gnPxnLgAHlaSon06gr+jwgTVWXtRAulRq7r9XVDQxHcMbwk2CagF95fH4N7JUkgQWideq0pDQ3e4VliAxymFqcE43bJkovBlO5oi+vO+gNUlk1mx3DIMhkunDhWbHaB9OShrJSdaluPnuno6O9Zpgx+HiRicixqnqrZwYB0uQFaZ8HEwfy5KrohGo88pIOzBnUC8ovnd3ttVQajgg1s0HXgv0dWluVgw5yDq5YDZqbm/nsZ6/39HyK+/TINMdHVK+uamisxpMszm0KiXiRBWEctcJcahVZeIOFgdfqzG9l6a4i6IxlleZlpA6zorfUqU1NN6L6gbnXJ7rElbb9oXLlPXo0iayCm5ubfVWzXv02itoxzfFRjapr9OipWOFooMTo0VMDTfZRy8yLGjKykV9ErvZPVaBa5N1V0W1CaWw8zLeDe00ocUwSzc3NrpN5FFVaHJNZFgM/zUnYSTU7evRUFi8+l7lz6zwP+Iqidkx6fNj7j9t06ccY29puprV1FpvPnemktXVWoDaPql7Ly8LUz8g/3OXTCByWEo2ZI0uPl7y7KrrZetrb7/Lt4H7G9Gonibgn8zgms76wP8nuQDN+/IW0ts7qbgM3lEqNkdQ3SY6Pyv7jfDDZ5tMl3VBNmzuPEWHDhjc856K8LEz9JJi3gfnAU7bPfPOzlcdzvQZZi5q14Kro5JEXpINbzKmalaEX4w86sIPu94g6mdmlor62P8nrFEcLdXWDmDjxkkj5Jzk+gtAOPU+drOyXblJbkDZ3djjx3/Sbl4WpH4NZDExR1R1sn/GqugPQlgJ9qcFtsspa1KzVPTvhOnjJ4Rqeq7QgjD/oZB7UkyrqZGb3Usti4Ge5SPGeRKvvz0mOj6BM357OqV9WeiFaCNrm1gLOeMeKg/Nc5qK8LEz9Dhz7DTAMcKrpn8dOTQZwCtJoPwUvD6JmkgcKJRUQM+jhSsbgcD/a2O1EwiAHS8V9OFYcpwemddiaHVmeeuh1imNc8bSSGh9utDuls+AeZmiz5AHR2jzMXJSXky79vMh+p6qOx/ep6qXJkJQerNVGZQRg2DxZ5UXUTAJJqv+CriyDMGqnVVqQwRZlFeendgu6QdfNS+2KKxZmIpHGvbE4qF0yaBvkYWd/JYJsuK18F/f+rFW3edi5KA+bySNFUxaRycAyVV0WP0nJoXIfjJd+1IDQ1HSj41kn9fWNTJiQ77NO/JCHaK3+bWChfI9EmIOl4j5LJCxqOaKyE8LWk18b5HmvVyXtjY2H0d5+l+u7JDmmsqynqPtg/FRkbvgmsJuILFDVL0XMI3P4rZ4bGrbvbrgFC86is3OzpGPtqAVibdw0z3DJg/rPSWXkhMpVWhKqprDnufdVhK0nPxVWUvUex1gKq35LUgWaF7VXGETaB6OqU1V1d+C0agoXkUNF5BURWSQi5zjcbxCRP5v3HxeRcbZ7PzCvvyIin41Svpeaq/Ks7fr6LXqkidvYH7fKyk/tkAf1X6UqrVRqRKR/WRqnARpEBRe2PpNiuJaXWh7VQFEQdz0lUe9ZeX8m7ZSTB7VXGGR24JiIlIAFwKeBJcCTwPGq+rItzZnAbqp6hogcBxylql8SkV2APwF7A9sA9wETVdXZUd1EpYoszFG/aRxSFqd4HUSc9koD2a2U4pLiwtSnEcJkKk57HWpdvRE34lYDJaFWyoP6tzch8QPHRORpr/8RsDewSFUXq+pG4BbgiIo0RwCzzN+3AQeLYTU9ArhFVTeo6mvAIjO/UHBabTQ13cQBB6zsMejTWO3HuZIL4l7tttoCMt37E9cqLWh9WpO/E3NJck9FnkL+hIHbxkK/DYduSMKl1r3tg9j7skVvkXQhhA1GVffw+h8B2wJv2f4vAT7ulkZVO0RkNdBoXn+s4tltnQoRkdOB0wG2374nMwiqY3XSrYr0p6NjHXPn1sWyyo/TrTbo5Or0/vPmjat5W4QxKOtwlkjK69N9Q10p8T0VeQn5EwaVGwv9rvshCduCu4ux0NZ2c277caWk6+amXyvo9QeOqerVqjpZVSePHDkycj6Vq/36+kZU1TT8x7PKj3MlV43EVeuTYViJxP29umIb1Hmwd8WFJPpH3LYFo42dNjhqrqXG3iTpgn8ssjv8MgiSxgVLge1s/8eY1xzTiEg9MBRoD/hs7LAPglJpCyo3CFbbEeI0EFbDrGp9MgwrkcTxvn5qjagxpfIIt3oplYZ7Ppem6sdoY2f7cp4XSrW+uKuEnwSzv89plrcDu0Qs+0lggojsIIbb0HHA7Io0s4Gp5u+jgQfU8EqYDRxnepntAEwAnohIRyQk1RHiWslVw6zyEmYiLMqPbnaCs0RS7fsG8ViKGlPKq8ys9PRGvfTrcb2ra60rHVl4dW2u68rr+V0o1frirhJ+B45NBV53uf1J4CFgo6rOi1S4yGEY4WhKwHWqeqGInA/MV9XZIjIAuBHYHVgFHKeqi81nzwWmAR3At1X1br/y4jxwLCsvlbj3ybjll+Z+nDjg5hFoh1fbVPO+YftCtX3H+V2FbbY5g4kTLw9Ec7V45JERjhEwknpnCN9Gtei5l1eao3qR+TGYxcCVwK8sF2ARGYVxXPLOUQrMEnEymCw6QlDX46x3rmcBv4gASb5XWBf2al3e3d/ViDyRRtul/c5R+2qtLZQgnzQn5aa8BzAeeFZEPiUiZ2GoouYRwS24NyGLKMd+BsCwaojeZFD0Uk0m1TaWmspN1x9W3RFUDeIV7yqttovr3YK8s7VHKUhfrVQdAjW1MRFqbzOlFzzdlFX1XeAMk7HcBywDPqGqS1KgLfdIMsqxE/zsPmFDbvQmg2LSUXudYlK1ts5yVcl52XCqDSfiFeU3rbZzDvEjrnthor6zl0cgOIfKT9vFN48SR17g50W2pYhcBZwCHIqx2fFuEflUGsT1JsRhlPVbBYZlGL3JoJikY4KTZLhs2ZUe9h7vM9erlX7dXXDTa7tRo6xz5u10qOtRwFHf2e/QL79Q+V1d79PSMjUxZwinvtHSchILFpwZazm1Cr+Nlk8DlwNfV9UO4B4RmQRcLiJvqOrxSRPYGxDXyspvFRh2o2YWZ5MkhSQDAbqf8eEG48z1oUP382Qy1XgIrl79b5Ytu7KMjrTbzthY6XwAVpSgl07wksiCh8rvNO/HI9HYJRbnzbzKsmVXerZ/X4GfDeaTqvpLk7kAoKrPquq+wAPJktZ7EJetw28VGHYVn4UdKUkkpbuOonZK2pY1ceLlNDXdmGnbpaFidZfIeu5pCiK9VdsulRKLm+ou7xs600JmwS6zQJxeZGGQRqBMC1H1wYUe2R3Bz6ypRPztGzfSdM+OSl9Q77EgruoGordLuL6Q//YPisSDXRbwh5udJU1bR+UqHvC1/WQV2rxWEFXtlHdbVrXtnsaG3KDHMsybN46WlpMQGUh9fSOGbajkmKdTxAG3sVt5PcxCI472r/XAl4UEExPcVlqjR0+lre3WssPKrHtJqzSCrv6K0Ob+8NpY6GbLyru6MYvNj3HD78iJlpZTqAzpJNKfnXe+zvfYitGjpzp4Cm6OwOCFONo/T/vUEtlo2dtgMZgog8J/x7vbyqZnh0zruOWgE0iaKrxahd9gz3qijYLe0O5+fTxIxAF3yaSEs42lfExbzMjrKOUoyNPCL+0jk2sWUTy63J5ZvfrfnnshDPQcwB0d71b1DkER1Agb5zEBWSLJSd7PSy3tPVFRUFk/pdLwHpI1xNfuaTBdvz7e0bHK9zk/77OeUBoaxia+mOgN+9T6HIOJcv632zPLll2Neyf0QmcqG8CCMo7e4K6cxia7WmAibnCqHyPGbD/sKqS49w4lvenRrY9bdpYgY8B946qzBJOWBNEbFn59zsgfZVUQfoVjwXkzHKQTkiWoEbY3uCvH4Qpe6wZVLzjVj+pG6uuHBGr3sHWTVhgiv8jObsck2CMOuI2TbbY5PdOo4rUa1dyOPifB+K14wjzjrqM1Vjl+4USSFnXDbD6s5dU5VK9O6G0nCVbCrR46Olax//4rPZ+NUjdpqXdGjTqBhQvP6mFnUd3I4sXnss8+rztsStWyjbBe42To0P1SiV7u9m5udNUK+pyR/847vxPIs8SOMF4mTtGNW1qmkqWo3RdQrUE0TwbVJFDN+0V5Ns369HNWyEvb5skrLCyKfTABMWrUCdTXD+lx3VrxuD3jpEKaOPFyX9XSqFEn0NQ0q+ZF3byjWnVCbzCoeqGa+olSN2mqd6LH6IuyeTY6elP08qDocyoyCOZZUgk3FVIQ1VJvEHXzjmrruDcYVL1QTf1EqZs0+3zUGH0gtLXdnNo47O2LGCf0ORXZ/PnzcyMyF8gPall9YSEpt+BaqBuvdzfU1CfhpEZLc8zX8rxTUyoyERkuIveKyELze5hDmkkiMk9EXhKR50XkS7Z714vIayLyrPmZFKb8WvDO6M0eTXmEnyddHtrDi4Y4w/04HdqVdy9Dr0Cnxm/nhXSa0kMtzDtxIxMJRkR+DqxS1Zkicg4wTFXPrkgzEVBVXSgi2wBPAU2q+q6IXA/coaq3hSnXHiqm2tVekpvI3M5ctzZ4Feq1eOHXlnlYwfvRENfqOA/vmgTyIj3UYsQHqDEJBjgCmGX+ngUcWZlAVReo6kLz9zJgBTAyLgKcVjxBV6lJB4f0On+kCEQZL4K0ZR6Ms340xKXfz8O7JoG8SA+jRp3A+PEXmnahN1m8+NzYxnIepOxKZMVgRqnqcvN3KzDKK7GI7A30B161Xb7QVJ1dLCINHs+eLiLzRWT+22+/7VpGGKaR9CD0mxR6w4DPC4K0ZR6Ms340xBWxOw/vmgTyspk4qcVpXiOiJ8ZgROQ+EXnR4XOEPZ0aOjpXPZ2IbA3cCJyiqlYEvh8AOwN7AcOBs10eR1WvVtXJqjp55Eh3ASgM00h6EAaZFGp9wOcFXi6s1iowD0dL+9EQ1wo9D++aFJKUHuxoa7uZhx8ewdy5wty5wiOPjOguJ6nFaV4lz8QYjKoeoqq7Onz+CbSZjMNiICuc8hCRIcCdwLmq+pgt7+VqYAPwB2DvMLQ5iZJhmEbSg9A5vEUyZfV1eNWjtQpsbDzMc/JOQzXhxUAsvb4xwRhnoERdobv1vc7Oda5nCSX97nGVkcYq3/BYO6UsiGhHRzv/+c+00PNMGORV8sxKRTYbmGr+ngr8szKBGJH4/g7cUGnMtzEnwbDfvBi0YLdO5hYqxmkCSlqfWy7OQ2VMM7+y8qiLzSv8mHlX1/u0t9/lql5JSzXhpuIBbOUDdHb3j7DMpZxRlfe5jo72Hu+V1oQdVxlprPKNvDb1uG5t5HZb0NTXD69qzOZV8szKi6wRuBXYHngDOFZVV4nIZOAMVT1NRE7EkE5esj16sqo+KyIPYBj8BXjWfGadX7mTJ0/WSy9d6ehNUl/fSFfXB4G9Z9L0Bqksq7HxMNezJ3qrF1CSCHKmj9v5KHF6b0XpT0l6jzkhyDkqcXpmPfzwCMcjBUqlRurrtwhVX2mcf+NehlFOU9ONPepZpD/GPGxnTP2orx9CR8eqQO+X9LivqfNgVLUdONjh+nzgNPP3TcBNLs9/KmrZXkH/mppuDBWILq0J216WX+DBKMcR9HVY9es+YXqp0apXTVQTaDNJ7zG/fJNWy7S13ezIXAA6O9u77wWtrzSiNbhHDTDuOUU46OhY5/Cem7oDeAZ5v7xGC+lzsci8REmvzVp5gRsDaWmZyty5da6dO2tdbC0giuozDtVENaqbpL3HvPJNWi0TRnUVpL7ScFV2Oz5ApH93OZXzTGenc+gqO4K8Xx7nrz7HYPLiDx8V3mfTuKs7s9bF1gKiuLLG0Z+qkQSill9pp/M6rsIt36THUthFkV/6NFyVjeC2f6BUauy+Vl/f6BqpHYKPzVpcJPa5YJd5FSWDwksEd0MtMdCsEVb1GUd/qkZ1E6X8oKdb+tkBkh5LYft60PqKKz5bXMdnOwXrdEItLhL7ZLDLWkZQY6wBqTkGmgTyHp4jbccMN1tTfX0jpVI4w7kX4gjHFLSvp+nIkkR72euqVBpOV9daVDfGln+1qCkjf4FyVHPKnaHlLA4zc0MtnFRZ3qZvAKUynXsQOp360OY8y/tVNadbBkUc9R60r0Mp0uQblQEm4UhTKfXkfVEUFIUEkzGqXQ0VbsneyEuQwyCI2pZOzzm5vlp5ublkx1knSdR7nG7G1YybNNyd84ZaC3aZCdaufSp3Gw+r3fyVlxhLeYSxc7p2vOqi9gWn5wz1SvmGPyuvNBxdknBhjtNrLQ+ee30BfYrBQP6iEccxEPPonpg1rBWqG7KaDLyiLETtC2H6yoYNb6ayKEliEo6TMWbhudcX0ecYDPRcqWQZWqVYDSUDr42DWU0GfmFPovaFMH3FSpv0oiSJSThOxljNuKuGjr4WxqlP2WB22kn0qqusf4a+NGsbhrOnTLgwEQV6witkR1PTTZnUp59dIupBc2FtMGkeklatoTqpPIDUx33Wc001iGqD6bMMxhrUeTAC591FsRaRh3atRBDjcHlcNClLHzY2HtTufi+IZ0L2XsC1Y0Sf7kzlpNg89smgKNyUQ8AuquctzHVn57tUumIWscTCw2nzWtZ68iAbKr3ionn1A7fNfbXcZ+JwB3ZWlW6O81VN9OmwyNtckwb6nA2mUl+atQ2kUi/v7OeffSesNd1xHr3rwtgl+uJkVIk46iBI2rQO5sp6rskCfYrBDB68Zw+DZtYeIUGj2CbVCYMwjrwex+oHJ0N2lowyDNPL82SUVh3GUQd5ivOVxlyTt4Vgn2IwTsh6pRusY0vZEb7VYnMnFFpaTvJkHMYJfVNzeRxrWNQSo8x64eMGpzpsaTmRhx8eEXs9xlEHQU6HhXQYd9JzTR77d58y8udxJ7+b4c8yPoYx9AZBkPhO3l5N5cjKIysKsjayhjVa5zFciHt/TcYZJW4vst7sRJNk/y68yAIgjwzGa9JJIqSH1wSxGYZXU5C0tTQ4sw7xkTWDiwPeJzbS7Y2VN8ZoRx4ZdxxIsn/XVKgYERkuIveKyELze5hLuk4Redb8zLZd30FEHheRRSLyZzFijdckvMTmJAy9QZ611AV5MpDGgaTOQw+K3mC491MlWWqZPKlpKhF2k2ne7BpuyKPdLisbzDnA/ao6Abjf/O+ED1R1kvk53Hb9Z8DFqroj8A5warUEZW38derwSXQYv2ftOu48GUjjgJM+XqQ/HR1rUpkQ8zgBhIW/TaPUK+x1FvJo13BDHu12WTGYI4BZ5u9ZwJFBHxQRAT4F3BbleSfktRMl0WGcJwgBerpw58lAGgdGjTqB0aOnYti3ML8rD9lKbkLM4wQQFpbEXV/f2OOe8W5ubvZv1IQUUIlqg9GmuXDN2mHJCVlttBylqsvN363AKJd0A0RkPtABzFTVfwCNwLuq2mGmWQJs61aQiJwOnA6w/fbGRFipg+3oWBf7+Q5xIIkTA8PkWZm2vn44HR1rqAw/UisTZFvbzSxffi2bJ8FOVN9zTJuEVFbrp6lasDZ1Otky3OyGlickpH8mTzU2Fz+1plfeWZxFFNeJnXEhMSO/iNwHjHa4dS4wS1W3tKV9R1V72GFEZFtVXSoi44EHgIOB1cBjpnoMEdkOuFtVd/WjafLkyXrnnd8JdSKk3Tjm11F7q/HQjlp+x0ceGWHbwe2NWjK85wkLFpzJsmVXUm5sFpyMz2nUcbXhZrwcM9yiRVh5B3HqqJXxlDsjv6oeoqq7Onz+CbSJyNYA5vcKlzyWmt+LgbnA7kA7sKWIWNLXGGBpULqCbmyEctWPnxotzf0BWSLNowHiVi8EZS61JJXlCW1tN9PaOouezMR5EZuG7a5aFZeXWtMv7yDSTx5V83EiKxvMbGCq+Xsq8M/KBCIyTEQazN8jgP2Al9UQueYAR3s974agnbpykvHrTG6Mq7Oz3bPT1IqHStpIe/DlSW9dqwizeAN/210cY6Naz71qvDz9nDqqZX5OyNt8kpUNZiZwq4icCrwBHAsgIpOBM1T1NKAJuEpEujAY4UxVfdl8/mzgFhG5AHgGuDZowW4BB+vrGymVtnAVVf06k1eHdbPn1MJ58VFRreifxLnnpVIjnZ09pZhSqbFQh8WAMBKJn5QY19gIEmDUD252Db+8/QKuxu22nsf5JBMJRlXbVfVgVZ1gqtJWmdfnm8wFVX1UVT+qqh8zv6+1Pb9YVfdW1R1V9RhV3RC0bDeRd8KESzxVP36rEf/9AT07TRIrmDwgDukjiT0jEydeguE1Zkc/83qBale/QSftIFKi29hoaZkair4kPff88vbz6orbbT2P80mfi0UW1ZXPrzP5ufQ6dZresPHOCXF09CT2jIwadQJNTX8oa/umpj/UvLQYB+JYFARxa7cM3E7SvJ25uUeQ6AxFX5Kuu0Hy9rJZxs383OeTNzJTlfXJ82CiuvLV1Q3snjhLpUYmTrykOx/re+HCs3oYk906TRTxPS+nBHohDsaZ1HkueXPjrAZxtmMcKslyN2znA9Oc2s9JtePmeRaFviTbvJq843Zbd5tPgMxUZX1OgokCawDYGYfqBz3SjRp1Avvvv5KmppsCrZi8VjBO6oo4VplpGM/jkD7yuGksblSjkoq7HeOSpjev2JWmphsDtZ+zc4BibQCOQncSSMKAHqdXppcEmZWqrAh2GQBJBikMc154Xd1AR1fbMHSkEXCxls8eTwtJ7s+I0o5ZBuL0CqDZ0DDWZCJ1OEUJcKKvGsnO7dla6dPG8RonutyNHvSyODI5QSRpK3ESsefNG+eornBzAY3jhL84V4JZ7FivlQ1rFqpVScXdjnGrJMO0h7uquHxDYhD6gnpSBVnY2Z9NwqsxCYwadYJHFPb0QzoVKrIASDtIYdhJIo4T/uJ+l7Q3ZNbahrVqGYR7e2kk9Y2bShIIrRYK2x5BjN1BVaZBHEzc6Fu48CzXZ8O2V1b7UdrabqajY12P61ltHi4YTACkHaTQbfIolRoTOeGv1neu59E90w/VMnqjvSpdrg1EZbCViwIgEuMO0x6WJGGkN4KQujGPIIuWIIzAjT63SA+WlOMEp+tZLXisciv3eol8KDNVXsFgAiBtg7MbE5g48ZKq6YjyLkmsxuzHNs+dW8/cuZLZbu0sMH78hVQeYyTSPzCjHzXqBOrrh7jej4PBRmXcQdujfCIG6Oxe7EQZW0bfcZ7S7IwgioYgzMIsqwWPWyQF1eDRFeJGYYMJiDTdW/1sGNXSEeZdktgd3FOf3llV3l7u3nm2zVQ62IR1uOnoWOV5v1oGG5VxB3W/j9OuYfUpJ0eASkbgRl+p1IjqB452ns1j8mf063ca9fU7U18/nFWrPsSqVS1l+QwYcCUDBjjT2dLS4nyjCnR2vkdHxzue5S5fXupBpxMGDBjAmDFj6NfPWToOi4LB5BR52a+RhHHTK2ZVlLzdDNSNjYflLnSGBWM1u6ni6qZQ7+6178G6Xw2ihlkJ6jAQp+Tp3qdKPSR0N/qsiA5eC7v339+XwYMH09jYiHE0VU+sW7cJ1Y09rov0Z4stmkK/mxc2bWpn/fo3AMdDgcsweLB32apKe3s7S5YsYYcddoiFvkJFlmPkIXBdFsc2R9l74aT2a2+/K7e2mbg2o7rte4jDrhbVXhdUDRunw4l7vXU52nLc6POz86xfv96TuRj0b0vPqbXOvB4vNmxYCvi7Hgc5VV5EaGxsZP369TFQZqCQYKpEUiqYvASuiyNYYNA8q8nbSeJraTnJMW0ebDNxBWEE+875EtDZfVZJHKrUzfmH699BJPA4XaPD1mc1GgIv5gLQr59x2ueGDUtR3YhIfxoatu2+HiecJKWeCM7c/N4tLAoJpgok6S0S1N0yaQknvWOb48nbjrTdy8MgrnodNeoExo+/0FyNd8XGXOz5J+VuHqfzTN68I/v1a2SLLXZj8ODJbLHFbokwF/CXTET6M2DA2MTK90PBYKpAkt4ieTmsKI5JoJIRArY8wck9NQ7mmbdJx464Jtcw/SAPKtdKxMXA8h5aqLm5OZF83dRxAwbsUMbcLrvsMnbccUdEhJUrVyZCixOKUDFVwD3ERfSQDBb8Qne43a+vb2T//dPrQH6IEmIjzrAcefYiCwund3HftV0eQqVWQp3kHS0tLTQ1hTfUiwhr1z6XiMps06Z2X3XcM888w7Bhw5gyZQrz589nxIgRrvk5vWPujkzuC0hSBeO3+naTcDo62nOxMrUQRcqLUzJMK6KAW3DSoBKDX1o3ScXNllXZP+Ko0zxKQLWATZuMjY+WvUR1I+vXv9F9PQzOO+88fvOb33T/P/fcc7n88pt81XG7774748aNi0R/NSgYTBVIUgXjJ/J7MbGsvaTsE1HQCTDIvTwY553gNPn/5z/TaGk5JbDqyk/N5cYgLPViJSr7R7V1mtdwPHlmes3NzYgI/fsb0sKQIXsxZMhe/PSnVwNdpgdYOEybNo0bbrgBgK6uLm655RaOPPJIJk2a5Ph5+eWXfXJMFpl4kYnIcODPwDjgdeBYVX2nIs1BwMW2SzsDx6nqP0TkeuBAYLV572RVfTZZqnsi6aCOXp4u48df6Bo11ctDK2k4qWKc4MUgk/BcSxJOk7+Td4/bHp8ge43cGYGx+93PEytonbqpFOPeFBnHmHHytGxpOYnVq//NxImXh84vbjQ3N9Pc3MzatfMZMmQv1qx5sux+MA+wcowbN47GxkaeeeYZ2tra2H333Rk7dizPPvtsTFTHi6zclM8B7lfVmSJyjvn/bHsCVZ0DTIJuhrQIuMeW5Huqels65G6G0+DI4jz3UaNOYMGCsxzPmAehre3mTHTrXpsoLfhJeUkdNpYUqo1mHUS68Io4vNkW4z5hB6lTL9f4uKTKON3v3c6RWbbsSoYO3S83tiU3T68ge1OccNppp3H99dfT2trKtGnTWLt2LQcccIBj2j/+8Y/ssssukcqJA1kxmCOAKebvWcBcKhhMBY4G7tYYg+pEWUXlZW+KhYkTLzH3elQ6GmhmYcS9JxwJVNdZhPsPCqd+47evxw4nKSyIdOHFIILs6QhSp15SSlxSZZySkHtfy67/O6GhYVvOOef0iqvRN14eddRRnHfeeWzatIk//vGPlEql3EowWdlgRqnqcvN3KzDKJ/1xwJ8qrl0oIs+LyMUi0uD2oIicLiLzRWT+22+/DTjrk1taTuoRcLFSv7tggXs47yxgDCBnL8Ak7BVB9N3ujg9jQxnanYzzyQbdDGaId7JDNDYe1sMWZ6xOy+M5uUlhcYar94Kfw4OXlBKXvTFO+5oXc8uTva5fv0bOP/+n3RJLtXtT+vfvz0EHHcSxxx5LqeRsg6vEb3/7W8aMGcOSJUvYbbfdOO200yKVHRaJuSmLyH3AaIdb5wKzVHVLW9p3VNUxmI6IbA08D2yjqpts11qB/sDVwKuqer4fTZabspuLr4W6ukGMHj2V1tZZvuoek8qq3ZKjIq2TCIO6ubrZYOrrG5kw4ZIYA2RW72YbNk+vunZSU0FwKSwP7tR+fSkOGuPsr8bpjU4SPBjOD12x12VUN+U40dXVxR577MFf/vIXJkyYEHv+cbopJ6YiU9VD3O6JSJuIbK2qy01mscIjq2OBv1vMxczbkn42iMgfgO+Goc1vddPV9T7Lll2NU2RWJ2RpfE7rJMKgqg3rd6V9qKOjvSp1YlpBN73y9Fp9u6mpgtKWh+Cmfn0pDhrj7K+jRp3A6tX/ZtmyK+nJZKqL0J1XvPzyy3zhC1/gqKOOSoS5xI2sVGSzganm76nAPz3SHk+FesxkSogROOdI4MUwhQdjCMGYS5LG5yDqmzh3MHu5ooZRbRhnlWzR43o16sQ0g266Xc9z6Jk4kMZu+LjLmDjxcpqabuzOz8ltOy8BTuPALrvswuLFi/nVr36VNSmBkJWRfyZwq4icCryBIaUgIpOBM1T1NPP/OGA74MGK528WkZEYPepZ4IwwhTutonrCCBxYifr6RkqlLRJXZYRxwYxr9RunkTduhpBm0E23PGvNuy0K0pCk4i7Dnp8RXaMn8mST6UvIRIJR1XZVPVhVJ6jqIaq6yrw+32Iu5v/XVXVbVe2qeP5TqvpRVd1VVU9U1Z6HUHugfBUFBp/ajLq6QWyzzemORs0JEy5JZWe4lwtmUpvJ4jTyxr3aTyvopleeeY93VaD3S5m1hj67k3+zR42WidjWpDFx4uWZTiZ+LphJwGtwhp1c42YIfuVH8TCLwjDSCj1TIBryHOC0L6IIdplTPPLICDo63GIVRfNa8/MCittTKy3PqFoP5JgHD7LehCTrMw9eZEEQJACmG2rCi6zWkfWg7+x0P1UuirgfZJNo3Bsc0/KMSsLDLC3kbfNub0AePPIsZDGPbD5G2ViEqm7kP/95lFNPbWbVqtXsueee3HjjjfTvHy2SQBj0WRUZuKtV4grsV83GQNX3XO9FEfeDRtMNogJKK8Bg0HJqLTimHUmeKdSbkEVQy2rLzCpAqNMxytOn/5YzzzyWRYsWMWzYMK699tpEabDQZxmMV+PHFdo8qc4VZQUUdywpt/eKayIIU3+1bNitZeaYFrKYqN3K7Ox0X/hVIonFg1O4/ksuuaQsTWUQTVXlwQef5IgjDgRg6tSp/OMf/4hMQxj0WQbj1fhxDPpqO1ep5Kwvdbvuh7gmYa/3inMicCunpWVqD+ZVy4bdWmaOaSHoWIpTynErs6PjHZcneiKJxUOQcP377Xci++333+y333/zn/8sZtWq1QwdOpj6+no2bWpnzJgxLF0a/qiAKOizNhivxo9jz0W1ncsIZHkKsMl2tR8TJ17i9ogn4trD4fVe6QQydN+hnSdDeVDde1/YW1MtgoyluG1ZbmWqBtuADcns3QoSrr/SBtPe/m73PeOgs/Sm/T7LYLwaP45BX23nSsLgHkd+Xu8VdyBDvwjFduaVN8Nu0Mmu2naJw4ictUOLH4KMpbgdPdzKFAkWXBKSWzwECdev2onqBq699gJ22mkHVq9eS0dHB/X19bz22nNsu220SM5h0WfdlP1cW6sddLXuOusGr/cKej581HKckV2gUTfkLQBp0nkkjSA0Gjv4neay6C79TmUOH/4gu+4a3Fs3Cea9ceNGPvrRj7Jp0yYWLlzoGlF57drNWzK+/OVzOPzwT3H00Z/h29++iD33PJgzzzzT8bnCTTkG+K0co66I7R2qVBpOff1AOjpW5XJlGAV+9RZnIEN7OYa5sKd6Io+2irQM93Gs2mvBxTuIlBe3OsqtzFWrPhQ6Hysva2/K2rXzQ+9NscMK17/lllt6husX6d9t8J8x4xuccsq5/OQnV/CxjzVx6qmnhi43CvqsBJMEamE1mDSSUrfUUt0GkWDiqKcgq3a/cuJe+WcFr/4B8amao260rLSLmBS6ngvjtVEyaLj+sGVaiFOC6bNeZBC/b32xp6HnPhogljoeNeoERo+eyuZouSVGj56aO+YC/l5tQQ+884OfB1oQr77e4sXmFvYHyGQvSiWc9qZAl3m9HBZjsKQP1Y2mcb6dl19+mR133JGDDz7YN1x/v36NDBgwNraDzqKgz6rIkthBXexpKEecddzWdjOtrbPYrCbrpLV1Vq7OXrfgp9JxC2QK4erIz4gcRP3Vm7zYKut98eJz6exclwsVYOXeFK/rXsxol112Y/HixYHL7devMVWGUok+K8EkIW0kvRrMYjdzNYizjmtNOvSKiBDkwDuv97L6QUvLSYgMpL6+EadgnUEWPL0pQrSTxOYWz6+aRd/GjStZt+551q6dz7p1z7Npk1vMwM2wpIgg18Mwo7gRt8mkz0owSUgbSZ4uWV8/nI6ONVj7YmohZlWcddybpMMgLthu77VgwZllJzh2drZTVzeIpqYbe/SDoIbvPLl4VwNnydANyrx547oly6A2MZF22trWMHRoCZHN6ivAU1JoaNjW0R7S0NDTXdhunK+8niRUlfb2dgYMGBBbnn2WwSSxCSquvSZtbTc7Hjlcibx5+9hhSFfxeX4l0V5ZIciBd07v1dZ2s+PxwG79wG/Bk/f9L2ERdrFhLdJWr/43ra2zehzu19JyIg0NY8vq5Z13zmTdutNYuXJH7AogkXYaGsZ4ltfZ2UVHxzuodiJSor5+GKXSCipPjO/s3GhKRfZ2Fvr1a6RUagn1jmExYMAAxozxfo8w6LMMJindc7WrweD7PwzkZQXvLG31ZC5R67j32grewDjwbvNkItKfjo51zJ1bVzbxG2ozZxWG29HVm8spZyJB7GO1xoDcFiGlUiP19Vs43uvqep9ly66mZ191tolt2PAiGzac5VB6vF53znX/2djyTwuZuCmLyDFAM9AE7K2qjr7DInIocAmG69A1qjrTvL4DcAvQCDwFnKQBFJSVbsp5HEBuLq5uiHvzXhQEZ4olmppmRa7jPLZXHPBShcJmd9uWlpNwYzBh+4GfK3UtuYVb8KPZ3SXbH1a9pLWJNm+I6qacFYNpwlBGXgV814nBiBGTYQHwaWAJ8CRwvKq+LCK3An9T1VtE5ErgOVW9wq/cWjhwLMwgyMuAD84Ua2tvRRbwmsAAl3oWRxuMF/z2v9TqROq1CHHvpyWcpO1yGPVSi4w3DtTUPhhVbVHVV3yS7Q0sUtXFpnRyC3CEiAjwKeA2M90s4MjEiE0ZXjYFkf5mNOV8efsEVdPVor0kbXg5MzjtrwFhm23OiBRTzut6rTpVeHnvue1P2mab0x3qtRxWvfQmr7s0kOlOfhGZi7sEczRwqKqeZv4/Cfg4hmrtMVXd0by+HXC3qu7qUsbpwOnm312BF2N+jTgxYuhQurbairEi5cy/q4uOt9/mrdWrWZUVccAIYGXlxfHj+Wh9PZ4uLqp0rVjBGwnT70hfjuBLn1tddnSwcfFiXhg6lOGNjWxbX0//jg42trezNEqdDh3K8Mp+poquWMHrq1ezyo+OsOXFhKrb163+7NcrnwnRd2u+/3lgrKqODPtQYkZ+EbkPGO1w61xV/WdS5VZCVa8GrjZpmh9FzEsLIjL/3XfzTV/e66+gLzoK+qpDQV9PJMZgVPWQKrNYCmxn+z/GvNYObCki9araYbteoECBAgVyhDzv5H8SmCAiO4ixw+g4YLYaOr05wNFmuqlAahJRgQIFChQIhkwYjIgcJSJLgH2AO0XkX+b1bUTkLgBTOvkG8C+gBbhVVV8yszgb+B8RWYThqnxtwKKvjvE1kkBBX3Uo6KsOBX3VoaCvAn0qXH+BAgUKFEgPeVaRFShQoECBGkbBYAoUKFCgQCLodQxGRI4RkZdEpEtEXF3yRORQEXlFRBaJyDm26zuIyOPm9T9LzCFMRWS4iNwrIgvN72EOaQ4SkWdtn/UicqR573oRec12b1La9JnpOm00zLZdz0P9TRKReWY/eF5EvmS7l0j9ufUn2/0Gsz4WmfUzznbvB+b1V0QkkYBTAej7HxF52ayv+0VkrO2eY1unTN/JIvK2jY7TbPemmv1hoYhMzYi+i220LRCRd233Eq0/EblORFaIiOMePzHwW5P250VkD9u9ZOtOVXvVByO+2U7AXGCyS5oS8CowHugPPAfsYt67FTjO/H0l8LWY6fs5cI75+xzgZz7phwOrgEHm/+uBoxOsv0D0Aetcrmdef8BEYIL5extgObBlUvXn1Z9sac4ErjR/Hwf82fy9i5m+AdjBzKeUAX0H2frY1yz6vNo6ZfpOBi5zeHY4sNj8Hmb+HpY2fRXpvwlcl2L9fRLYA3jR5f5hwN0YUVU/ATyeVt31OglG8x+G5ggz36D5H40RqSDoQRfVIix93chL/anqAlVdaP5ehhEPPfQu5BBw7E8Vaex03wYcbNbXEcAtqrpBVV8DFpn5pUqfqs6x9bHHMPaXpYUg9eeGzwL3quoqVX0HuBc4NGP6jgf+FDMNrlDVh8AzysARwA1q4DGMfYRbk0Ld9ToGExDbAm/Z/i8xrzUC76rhIm2/HidGqepy83crMMon/XH07KwXmqLuxSLSkBF9A0Rkvog8ZqnvyGH9icjeGKvOV22X464/t/7kmMasn9UY9RXk2TTos+NUjBWvBae2zoK+L5rtdpsYIaLCPJsGfZiqxR2AB2yXk64/P7jRn3jd1eR5MJKTMDRu8KLP/kdVVURc/cTNVcZHMfYCWfgBxsTaH8Ov/Wzg/AzoG6uqS0VkPPCAiLyAMWlWjZjr70ZgqqpaYZyrrr/eDBE5EZgMHGi73KOtVfVV5xwSw+3An1R1g4h8FUMa/FTKNATBccBtqmoPz5yH+ssENclgNOdhaLzoE5E2EdlaVZebE+AKt7TAscDfVbX7cBDb6n2DiPwB+G4W9KnqUvN7sRhBS3cH/kpO6k9EhgB3Yiw6HrPlXXX9OcCtPzmlWSIi9cBQjP4W5Nk06ENEDsFg4geq6gbruktbxzlB+tKnqvYjXa/BsMVZz06peHZujLQFos+G44Cv2y+kUH9+cKM/8brrqyqyLMPQzDbzDZJ/D12uOala9o4jiT86tC99IjLMUi2JyAhgP+DlvNSf2aZ/x9A731ZxL4n6c+xPHnQfDTxg1tds4DgxvMx2ACYAT8RAUyj6RGR3jPOZDlfVFbbrjm2dAX1b2/4ejhHdAwzp/jMmncOAz1Au8adCn0njzhjG8nm2a2nUnx9mA182vck+Aaw2F1rJ112cHgN5+ABHYegSNwBtwL/M69sAd9nSHYZxoNmrGKtc6/p4jAG+CPgL0BAzfY3A/cBC4D5guHl9MsapnVa6cRgrjLqK5x8AXsCYGG8CtkibPmBfk4bnzO9T81R/wIkYR0I+a/tMSrL+nPoThurtcPP3ALM+Fpn1M9727Lnmc68An0toXPjRd585Xqz6mu3X1inTdxHwkknHHGBn27PTzHpdBJySBX3m/2ZgZsVzidcfxiJ0udnnl2DY0M4AzjDvC/A7k/YXsHnXJl13RaiYAgUKFCiQCPqqiqxAgQIFCiSMgsEUKFCgQIFEUDCYAgUKFCiQCAoGU6BAgQIFEkHBYAoUKFCgQCIoGEyBAgUKFEgEBYMpUCBmiMh2YhwJMNz8P8z8f7KIrBbzWHCfPHYQh2MPROQ7IvKmiFyW9HsUKFAtCgZToEDMUNW3gCuAmealmRhxz14HHlbVwwJk8zPgYlXdEXgHY/McqnoxcF7cNBcokAQKBlOgQDK4GPiEiHwb2B/4ZdAHzTA2SR97UKBA4qjJYJcFCuQdqrpJRL4H/B/wGfN/j3Qi8qyqTqq4nMaxBwUKJI5CgilQIDl8DiNG1K5uCRyYS4ECvQYFgylQIAGIyCTg0xhH1H6nIhqwH7qPjTD/JxHCv0CBxFEwmAIFYoZpQ7kC+Laqvgn8ggA2GBG5QUT2ViMCbdLHHhQokDgKBlOgQPz4CvCmqt5r/r8caKL8lEjAsMHY/u4GLDN/nw38j4gswrDJXJsYtQUKJITCyF+gQMxQ1asx3JKt/53AHiIyBdirIu0k6D6Bc6GqLjGvLwb2TofiAgWSQSHBFCiQHjYCuzpttFTVNap6jF8GIvId4AfAmgToK1AgVhQHjhUoUKBAgURQSDAFChQoUCARFAymQIECBQokgoLBFChQoECBRFAwmAIFChQokAj+P48LCa7ugllxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary([-1,1],[-1,1], y_train,lr.predict)\n",
    "plot_data(X_orig,y_train)\n",
    "plt.title(\"Example of overfitting, degree 6, with regularization, C=1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The decision boundary is much more reasonable with some regularizationg.\n",
    "Change the value of `C` above to try more or less regularization. C must be strictly positive. Values less than 1 maximumize regularization while large values minimize regularization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reduce the degree of the polynomial\n",
    "A degree 6 polynomial may be more than is required! We can reduce the values to limit the model.\n",
    "To do this, we will need to regenerate our mapped data and refit the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original shape of data: (500, 2)\n",
      "Shape after feature mapping: (500, 6)\n"
     ]
    }
   ],
   "source": [
    "print(\"Original shape of data:\", X_orig.shape)\n",
    "degree = 2\n",
    "mapped_X =  map_feature(X_orig[:, 0], X_orig[:, 1],degree)\n",
    "\n",
    "print(\"Shape after feature mapping:\", mapped_X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fit score: 0.968\n"
     ]
    }
   ],
   "source": [
    "# create and fit the model using our mapped_X feature set.\n",
    "lr = LogisticRegression(penalty='none', max_iter=1000, C=1)\n",
    "lr.fit(mapped_X,y_train)\n",
    "\n",
    "# print an evaluation of the fit, 1 is best.\n",
    "print(\"fit score:\", lr.score(mapped_X, y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary([-1,1],[-1,1], y_train,lr.predict)\n",
    "plot_data(X_orig,y_train)\n",
    "plt.title(\"Example of overfitting, degree 2, with no regularization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad! Of course, in this case, we knew ahead of time the data was quadratic and that a degree two polynomial would be a good choice. Try varying `degree` above to see the impact of polynomial degree on overfitting."
   ]
  },
  {
   "cell_type": "code",
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